The relationship of one quantum parameter such as polarisation, phase, etc. between photons in an entangled photon pair is fixed, although the quantum parameter for a single photon is not defined until it is measured. For example, a photon pair entangled by polarisation may emit two photons of the same or opposite polarisation. By measuring the polarisation of one of the photons in any given basis, the polarisation of the second photon becomes defined in the same basis. Thus, the polarisation of either photon is not fixed until the polarisation of one of the photons is measured.
Entangled photon pairs have been found to be particularly useful in the field of quantum cryptography. In quantum cryptography, a key may be sent by randomly varying a quantum parameter of a sequence of photons.
In the quantum key distribution protocol described by A. K. Ekert in “Quantum Cryptography Based on Bell's Theorem” Phys. Rev. Lett. 67, 661 (1991), a single source is used to send one photon of the entangled photon pair to a receiver “Alice” and the other state to receiver “Bob”. If a key is transmitted to both Alice and Bob, Alice knows what Bob has measured since Alice's measurements actually fix the state received by Bob. However, if an eavesdropper “Eve” intercepts the photon on the way to Alice, the entanglement of the two photons is destroyed. Alice and Bob can test whether their photons are entangled or not, by making a Bell state measurement, as described in the paper by Ekert.
Entangled pairs of photons may be produced using spontaneous parametric down conversion in a non-linear optical crystal, as described by A. Aspect et al, Phys. Rev. Lett. 49 91 (1982). However, this technique has the disadvantages of requiring a relatively expensive laser system and cumbersome alignment of the laser, crystal and collection optics. Furthermore, there is a significant probability of generating two entangled pairs simultaneously, which limits the usefulness of such a source.
Another approach to producing polarisation entangled photons pairs based upon semiconductor quantum dots has been proposed by O. Benson et al in “Regulated and Entangled Photons from a Single Quantum Dot”, Phys. Rev. Lett. 84, 2513 (2000). A quantum dot which is excited so that it contains two electrons and two holes is said to be in the biexciton state. The quantum dot returns to the ground state by successive emission of a first photon, which occurs when the biexciton state decays to a single exciton state, and then a second photon, which occurs due to decay of the single exciton state. According to O. Benson et al, the first and second photons will have polarisation entangled states.
However, the applicant has found that for real quantum dots, the first and second photons are not entangled.
As explained above, in the biexciton state, a quantum dot comprises two electrons and two holes. The two electrons have opposite spins and the two holes have opposite spins.
A photon is only emitted if an electron and a hole radiatively recombine. For radiative recombination, the z-component of the total win angular momentum of the recombining electron and hole must be equal to +1 or −1. Thus a Sz=+1/2 electron can recombine with a Jz=−3/2 heavy hole to produce a σ− circularly polarised photons, while a Sz=−1/2 electron can recombine with a Jz=+3/2 heavy hole to emit a σ+ circularly polarised photon.
Thus, there are two paths by which the bi-exciton state can decay to the ground state dependent on which electron hole pair recombine first. These two possible decay paths are equally probable and are only distinguishable from each other by a single property, the polarisation of the emitted photons. Thus, the quantum mechanical description of the first and second photons is a superposition of the two possible outcomes until the polarisation of one of the photons is measured, at which time the decay path that was taken is determined and the polarisation of the second photon also becomes well defined.
The above process is only believed to happen if the single exciton level is degenerate, i.e. the energy separation between the single exciton level and biexciton level is the same regardless of the decay path.
In the device described by Benson et al., as no care is taken to ensure degeneracy of the exciton level, the single exciton level of the quantum dot is believed by the applicant to be a split non degenerate level.